Physics TutorPhysics Tutor
62 physics topics explained at three levels, with formulas, figures and quizzes.
Mechanics
Motion in a Straight LineHow far, how fast, how soon: position , velocity and acceleration , the language for describing how things move along a straight line.
Vectors and Relative MotionArrows with a size and a direction: adding and resolving vectors, the relative-velocity rule , and why a boat aimed straight across a river lands downstream.
Free FallMotion under gravity alone: every body gains the same 9.81 m/s of downward velocity each second (), so from rest and , and a heavy ball and a light ball land together.
Projectile MotionThrows, kicks and jumps: a curved path split into two straight-line motions, a steady sideways motion with and a free fall with .
Newton's Laws of MotionWhy things start, stop and turn: force , mass and the three laws that connect them, with at their centre.
Friction and Inclined PlanesFriction resists sliding: at rest it can reach , while sliding it is . On a slope of angle a block sliding down accelerates at , whatever its mass.
Circular MotionWhy anything moving in a circle is always accelerating toward the centre, even at constant speed: , supplied by a real inward force .
Momentum and CollisionsMomentum : why the total momentum of colliding bodies never changes, while their kinetic energy sometimes does.
Rotational Dynamics and TorqueHow forces make things turn: torque , moment of inertia and Newton's second law for rotation, .
Static Equilibrium and LeversWhy things stay put: the forces must cancel, , and so must their turning effects, , on seesaws, levers, beams and objects that might tip over.
Angular Momentum and Its ConservationWhy a skater spins faster when she pulls her arms in: angular momentum stays constant unless an outside torque acts.
Gravitation and OrbitsWhy planets and satellites keep falling without ever landing: Newton's inverse-square law and Kepler's three laws of orbits.
Energy & Oscillations
Work, Energy and PowerWork , kinetic energy , potential energy and power : how forces transfer energy, and why the total is conserved.
Simple Machines: Levers, Pulleys and GearsHow levers, pulleys and gears trade force for distance: the mechanical advantage , the work balance of an ideal machine, and the efficiency of a real one.
Elasticity: Hooke's Law, Stress and StrainWhy a spring stretches in equal steps, , where that rule stops, and how stress , strain and Young's modulus describe any elastic material.
Simple Harmonic MotionSprings and pendulums: a restoring force proportional to the displacement, , gives a steady oscillation whose period does not depend on the amplitude.
Damping and ResonanceWhy real oscillations die away as , how damping ranges from light through critical, , to heavy, and how small pushes in rhythm build up a resonance of amplitude .
Fluids
Fluid Pressure and Pascal's PrinciplePressure grows with depth as , and a liquid passes any added push undiminished to every point, so a small force on a narrow piston can lift a car.
Buoyancy and Archimedes' PrincipleWhy things float or sink: a fluid pushes up on a body with the weight of the fluid it displaces, .
Bernoulli's PrincipleWhere a flowing fluid speeds up, its pressure drops: continuity, , and Bernoulli's equation, , in a Venturi tube.
Drag and Terminal VelocityWhy falling bodies stop speeding up: drag grows with speed, as , until it balances the weight at the terminal velocity . Viscosity , parachutes and streamlining complete the picture.
Waves & Sound
Wave BasicsA wave carries energy from place to place while the medium only oscillates where it is; its speed, frequency and wavelength are tied by .
Sound and the Doppler EffectWhy a passing siren drops in pitch: motion squeezes or stretches the waves that reach you, so a source approaching at is heard at , where is the speed of sound.
Loudness, Intensity and DecibelsWhy sounds fade with distance, , and how the decibel scale squeezes a vast range of intensities into everyday numbers.
Standing WavesWhy a guitar string sings only certain notes: waves trapped between two fixed ends must fit a whole number of half-wavelengths, , so only the frequencies survive.
Interference and SuperpositionWhen waves overlap, their displacements simply add, : depending on the path difference they reinforce each other or cancel out, and at slightly different frequencies they beat.
Optics
Reflection and RefractionLight leaves a mirror at the angle at which it arrives, , and bends at a boundary by Snell's law, , because its speed changes; inside glass or water, beyond the critical angle , it is trapped by total internal reflection.
Prisms, Dispersion and ColourEach colour has its own refractive index , so a prism fans white light into a spectrum and raindrops send a rainbow back at about 42°; coloured lights add, while paints subtract.
Lenses and MirrorsA thin lens or a curved mirror of focal length forms an image at the distance given by , with magnification ; a converging lens makes it real and inverted when the object is beyond the focus, virtual, upright and enlarged when it is inside.
The Eye, Cameras and TelescopesHow the eye focuses with a power of about 60 D while a camera moves its lens, how glasses correct short and long sight, and how magnifiers, microscopes and telescopes enlarge the angle under which we see things.
Diffraction and the Double SlitLight passing through two narrow slits a distance apart makes bright fringes where and dark ones in between: the classic experiment that shows light behaving as a wave.
Polarization of LightLight's electric field vibrates across the beam, in a direction called its polarization. A polarizer passes half of unpolarized light, , a second one at an angle passes , and glare reflected near Brewster's angle is polarized: the physics of sunglasses, LCD screens and 3D cinema.
Heat & Thermodynamics
Temperature and HeatTemperature , heat and specific heat capacity : why a hot body cools and a cold one warms until they match, and how much energy that takes, .
Thermal ExpansionWhy bridges have gaps, thermostats click and lakes freeze from the top: most materials grow when they are heated, by .
Phase Changes and Latent HeatWhy melting ice and boiling water soak up heat without getting any warmer, and how much heat each change of state takes: , with and for water.
Conduction, Convection and RadiationThe three ways heat travels: conduction through matter, ; convection with moving liquids and gases; and radiation, mostly infrared, which crosses even empty space, .
Kinetic Theory of GasesPressure and temperature explained by countless molecules flying, colliding and bouncing off the walls: their impacts explain , and the temperature measures their mean kinetic energy, .
First Law of Thermodynamics and Heat EnginesEnergy is conserved, , and a heat engine turns part of the heat flowing from hot to cold into work, but never all of it: at best the share .
The Second Law of Thermodynamics and EntropyWhy heat flows from hot to cold, why a gas spreads out and never gathers back by itself, and how entropy, , gives time its direction.
Electricity
Electric Charge and Static ElectricityElectric charge comes in two signs and in whole multiples of the elementary charge, ; rubbing only moves electrons from one body to another, so the total is conserved, and a charged body attracts even neutral ones by polarising them.
Coulomb's LawTwo point charges and a distance apart push or pull on each other with equal and opposite forces of size : repulsive for like charges, attractive for opposite ones.
Electric Field and PotentialA charge fills the space around it with an electric field , the force on each coulomb, and a potential , the energy of each coulomb: a positive charge is pushed along , from high to low .
CapacitorsTwo plates that store separated charge, , and energy, ; charged through a resistor, they fill quickly at first and then ever more slowly, at a pace set by .
Electric Current and ResistanceWhat an electric current really is, why the electrons crawl at a drift speed while the signal races, and how a wire's material, length and thickness set its resistance, .
DC Circuits and Ohm's LawHow a battery's emf drives a steady current through resistors, and how voltage, current and resistance are tied together by Ohm's law, .
Electric Power and Energy at HomePower is how fast an appliance takes energy, the meter adds up the energy in kilowatt-hours, and fuses and breakers keep the current low enough for the wiring to stay cool.
Magnetism & Electromagnetism
Magnetic Fields of Magnets and CurrentsWhere magnetic fields come from: magnets, Earth and every electric current. Round a long straight wire the field circles the wire and weakens with distance as .
Magnetic Force on Moving ChargesA magnetic field pushes a moving charge sideways, , so it bends the path into a circle of radius without ever changing the speed.
Electromagnetic InductionHow a changing magnetic flux through a coil induces an EMF : Faraday's law, Lenz's law for its direction, and the generator.
Motors, Generators and TransformersHow the force on a current in a magnetic field drives motors, how a coil spinning at generates an alternating EMF , and how a transformer changes the voltage in the ratio of its turns, .
Electromagnetic WavesLight, radio and X-rays are travelling ripples of electric and magnetic fields, and , that all cross empty space at ; they differ only in wavelength, with .
Modern Physics
Special RelativityWhy moving clocks run slow, , moving rulers shrink, , and nothing with mass can reach the speed of light , where the Lorentz factor grows without limit.
Gravity as Curved SpacetimeGeneral relativity: mass and energy curve spacetime, so clocks near a mass run slow, , and light bends by . A mass squeezed inside becomes a black hole, and accelerated masses send out gravitational waves.
Blackbody Radiation and the QuantumWhy hot things glow, why their colour shifts from red to white as the peak wavelength shortens and the radiated power grows as , and how explaining that glow forced Planck to invent energy quanta, .
Photoelectric EffectLight knocks electrons out of a metal one photon at a time, each photon carrying : the colour decides whether it works (), the brightness only how many electrons leave.
Atomic Models: the Bohr AtomElectrons on fixed energy levels, in hydrogen: each jump between two levels emits or absorbs one photon whose energy equals their difference, so every atom shines in its own sharp colours, the fingerprint in its spectrum.
Semiconductors, Diodes and LEDsWhy silicon is neither a metal nor an insulator: the band gap , doping and the p–n junction behind diodes, solar cells, transistors and LEDs, whose colour follows .
Radioactivity and Half-LifeUnstable nuclei decay at random moments, yet the number of undecayed nuclei in a large sample halves in a fixed time, the half-life : .
Fission, Fusion and E = mc²Splitting heavy nuclei and fusing light ones both release energy, because the products are more tightly bound and slightly lighter: the lost mass leaves as the energy .
Wave–Particle DualityElectrons and photons travel like waves but are detected like particles: sent one at a time through two slits, they land as single dots that build up fringes set by the de Broglie wavelength .
Schrödinger's Equation and TunnellingThe wavefunction gives the odds of finding a particle through , and the Schrödinger equation shapes it: in a box only the energies are allowed, and a barrier higher than the particle's energy can still be crossed, with a probability that falls as with the width .
Particles and Forces: the Standard ModelEverything around you is built from a handful of quarks and leptons, such as the of a proton, held together by forces that act by trading messenger particles: a carrier of mass reaches only about .